Thanks. One more question. I have not had to find intersections in a long time. What if I had something simple like

seems I forgot how to find the roots when I have a power higher than 2.

The "rational root" theorem says that any rational number satisfying this equation must be an integer that divides 2. That tells you that the only possible rational roots are 1, -1, 2, and -2. Try those to see if there is a rational root.

If not, then you will need to use "Ferrari's cubic formula" that ADARSH links to.